Space of modular forms of level 441 and weight 6

• Label: 441.6
• Level: 441
• Weight: 6
• Dimension: 26583
• Nonzero newspaces: 20
• Sturm bound: 84672
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(84672\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(441))\).

	Total	New	Old
Modular forms	35760	27020	8740
Cusp forms	34800	26583	8217
Eisenstein series	960	437	523

Trace form

26583 * q - 36 * q^2 - 72 * q^3 - 218 * q^4 + 93 * q^5 + 111 * q^6 + 62 * q^7 - 657 * q^8 - 474 * q^9 - 3201 * q^10 + 549 * q^11 + 2280 * q^12 - 191 * q^13 + 2166 * q^14 + 4440 * q^15 + 11802 * q^16 - 3729 * q^17 - 14112 * q^18 - 10817 * q^19 - 41607 * q^20 - 6894 * q^21 - 18714 * q^22 + 2577 * q^23 + 23529 * q^24 + 40404 * q^25 + 53841 * q^26 + 19992 * q^27 + 20214 * q^28 - 1773 * q^29 - 61056 * q^30 - 86615 * q^31 + 7062 * q^32 + 46368 * q^33 + 136290 * q^34 + 61233 * q^35 + 78783 * q^36 - 44931 * q^37 - 67404 * q^38 - 68808 * q^39 - 128883 * q^40 - 198999 * q^41 - 108246 * q^42 - 59503 * q^43 - 135993 * q^44 + 31362 * q^45 - 2985 * q^46 + 69927 * q^47 + 411279 * q^48 - 123042 * q^49 + 502851 * q^50 + 93360 * q^51 + 304031 * q^52 - 280347 * q^53 - 721467 * q^54 + 134430 * q^55 + 185412 * q^56 - 142902 * q^57 + 95181 * q^58 + 238359 * q^59 + 907092 * q^60 - 310894 * q^61 + 407349 * q^62 + 317532 * q^63 - 572927 * q^64 + 22131 * q^65 + 79962 * q^66 - 500799 * q^67 - 1179312 * q^68 - 671322 * q^69 + 591861 * q^70 + 532011 * q^71 - 671397 * q^72 + 1279009 * q^73 + 1018689 * q^74 + 194304 * q^75 + 733942 * q^76 + 166095 * q^77 + 1161738 * q^78 - 1217019 * q^79 - 2328138 * q^80 - 747138 * q^81 - 2376234 * q^82 - 1431675 * q^83 - 781668 * q^84 - 926577 * q^85 - 1526415 * q^86 - 1232268 * q^87 + 498057 * q^88 + 263751 * q^89 + 697044 * q^90 + 912377 * q^91 + 4806654 * q^92 + 2325378 * q^93 + 4003074 * q^94 + 3203181 * q^95 + 2734188 * q^96 + 505714 * q^97 - 2097708 * q^98 - 187872 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(441))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
441.6.a	\(\chi_{441}(1, \cdot)\)	441.6.a.a	1	1
		441.6.a.b	1
		441.6.a.c	1
		441.6.a.d	1
		441.6.a.e	1
		441.6.a.f	1
		441.6.a.g	1
		441.6.a.h	1
		441.6.a.i	1
		441.6.a.j	1
		441.6.a.k	1
		441.6.a.l	2
		441.6.a.m	2
		441.6.a.n	2
		441.6.a.o	2
		441.6.a.p	2
		441.6.a.q	2
		441.6.a.r	2
		441.6.a.s	2
		441.6.a.t	2
		441.6.a.u	2
		441.6.a.v	4
		441.6.a.w	4
		441.6.a.x	4
		441.6.a.y	4
		441.6.a.z	4
		441.6.a.ba	6
		441.6.a.bb	6
		441.6.a.bc	6
		441.6.a.bd	6
		441.6.a.be	8
441.6.c	\(\chi_{441}(440, \cdot)\)	441.6.c.a	4	1
		441.6.c.b	24
		441.6.c.c	40
441.6.e	\(\chi_{441}(226, \cdot)\)	n/a	162	2
441.6.f	\(\chi_{441}(148, \cdot)\)	n/a	400	2
441.6.g	\(\chi_{441}(67, \cdot)\)	n/a	392	2
441.6.h	\(\chi_{441}(214, \cdot)\)	n/a	392	2
441.6.i	\(\chi_{441}(68, \cdot)\)	n/a	392	2
441.6.o	\(\chi_{441}(146, \cdot)\)	n/a	392	2
441.6.p	\(\chi_{441}(80, \cdot)\)	n/a	132	2
441.6.s	\(\chi_{441}(362, \cdot)\)	n/a	392	2
441.6.u	\(\chi_{441}(64, \cdot)\)	n/a	690	6
441.6.w	\(\chi_{441}(62, \cdot)\)	n/a	552	6
441.6.y	\(\chi_{441}(25, \cdot)\)	n/a	3336	12
441.6.z	\(\chi_{441}(4, \cdot)\)	n/a	3336	12
441.6.ba	\(\chi_{441}(22, \cdot)\)	n/a	3336	12
441.6.bb	\(\chi_{441}(37, \cdot)\)	n/a	1392	12
441.6.bd	\(\chi_{441}(47, \cdot)\)	n/a	3336	12
441.6.bg	\(\chi_{441}(17, \cdot)\)	n/a	1128	12
441.6.bh	\(\chi_{441}(20, \cdot)\)	n/a	3336	12
441.6.bn	\(\chi_{441}(5, \cdot)\)	n/a	3336	12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(441))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(441)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 1}\)